Statistical method,under computer control,for the manufacture and test of mass produced articles



Sept. 1, 1970 E DEGER ET AL 3,526,836

STATISTICAL METHOD, UNDER COMPUTER CONTROL. FOR THE MANUFACTURE AND TEST OF MASS PRODUCED ARTICLES Filed Jan. 23, 1968 5 Sheets-Sheet l ffm/mw if.: wrmw INVENTORS AT YQRIIEY Sept. 1, 1970 E" DEGER ET AL 3,526,836 STATISTICAL METHOD, UNDER COMPUTER CONTROL. EOE THE MANUFACTURE AND TEST OF Filed Jan. 25 1968 MASS PRODUCED ARTICLES 3 Sheets-Sheet 2 /lv VEN ron S sept. 1, 1910 Filed Jan. 25, 196

E. DEGER ET AL STATISTICAL METHOD, UNDER COMPUTER CONTROL, FOR THE MANUFACTURE AND TEST OF MASS PRODUCED ARTICLES 3 Sheets-Sheet l [NVM/rafa Erturle Deger'c ,1 John B.

United States Patent Olce 3,526,836 STATISTICAL METHOD, UNDER COMPUTER CON- TROL, FOR THE MANUFACTURE AND TEST OF MASS PRODUCED ARTICLES Erturk Deger, West Lafayette, and John B. Schultz, Indianapolis, Ind., assgnors to RCA Corporation, a corporation of Delaware Filed Jan. 23, 1968, Ser. No. 699,967 Int. Cl. G01r 31/02 U.S. Cl. 324-158 6 Claims ABSTRACT OF THE DISCLOSURE Samples of lots of the different components needed for the manufacture of mass produced articles are tested to determine the values and their statistical distribution of parameters of interest of each such lot. This information is employed to calculate the distribution of the values of parameters of products expected to be made from these components, and the test limits to be employed in checking these parameters. If the calculated parameters indicate that a relatively low percentage of the products will meet acceptable performance criteria, one or more of the lots of components must be replaced and in this case the calculations based on the statistical information are used t indicate which lot or lots to replace and which parameters of the replaced lots are unacceptable.

BACKGROUND OF THE INVENTION The manufacture of mass produced articles involves, among other things, the design of the article, the procurement of material, the production of the article and the control of the quality of the article. In any factory of reasonable size, these functions-design, procurement, manufacture and quality control, are carried out by separate departments which do not always have common interests. For example, in times of lgreat demand for a product, those charged with production may relax efiiciency standards in the interest of obtaining a higher level of production. Conversely, quality control personnel sometimes call for a level of quality control which is neither required nor economic for a particular product. As a third example, those charged with the design of a product may, based on the belief that a low level of skill is available in the factory, call for relatively expensive parts to be assembled, whereas cheaper componentsthose with looser tolerances, could be used instead In brief, because there is sometimes a lack of reliable information on which to base sound production decisions and because the different departments charged with the responsibility for manufacture may have interests which do not coincide, the finished product often is not optimal in the sense that it is not, for example, the least expensive way of making the product without adversely affecting its quality or performance.

The object of this invention is to provide a method and system for making mass produced articles which eliminates most of the disadvantages discussed above and which permits a product of a given level of quality to be produced at a substantially lower cost than was possible heretofore.

SUMMARY OF THE INVENTION According to one feature of the invention, based on the statistical properties of parameters of the lots of parts tentatively selected for the manufacture of mass produced articles, a determination is made as to whether or not the lots are suitable for such use. If not, a sufficient number of the lots are replaced to insure that the articles will be 3,526,836 Patented Sept. 1, 1970 acceptable in sufficient numbers to permit proceeding with the manufacture. According to another feature of the invention, at the same time that the statistical properties 0f the parameters of the lots of parts are measured, the performance expected of the articles is determined and based on these performance parameters, the test limits to be employed in checking the articles are determined and subsequently made use of in making such tests.

BRIEF DESCRIPTION OF THE DRAWING DETAILED DESCRIPTION At the present time, when specifying a part to be used in the manufacture of a mass produced article, the design engineer indicates the values of given parameters of that part and the maximum acceptable derivation from these values. For example, a resistor may be required to have a value of ohmsi5%. This manner of specifying components is not employed in the present invention. Instead, the parameters are required to have a certain type of distribution as, for example, Gaussian, uniform, triangular or other distribution, a certain range within which the central tendency of this distribution must lie, and other statistical properties. This is believed to be a more realistic and natural way of describing the parts and it also makes possible certain calculations and predictions discussed in detail shortly.

In the discussion which follows, first the invention is discussed in general terms. Later, specific examples are -given to illustrate how these principles are applicable to the manufacture of a specific article.

The flow chart of FIG. 1 shows some of the steps in the process, according to the invention, of manufacturing mass produced articles. Such an article may be made up of some number m of different elements where element A may consist of a transformer, element B of an integrated circuit package, and so on. These elements may be supplied by ditferent component manufacturers and arrive at some central point in the factory.

In the manufacturing process of the present invention, each lot of elements is tested, preferably by a sequential sampling technique, which in itself is well-known. (See, for example, A. Wald, Sequential Analysis, Wiley Publications.) This involves randomly selecting a sample, that is, a number of elements, from a lot of perhaps 500 to 1000 elements, and measuring the parameters of interest of these elements (some specific examples of such tests are given later). The size of the sample, that is, the number of the elements which must be tested to determine the characteristics of interest of the entire lot from which the sample was chosen, is not fixed but will depend upon the condition such as the amount of nonuniformity, of the elements of the lot. However, in general, the sequential sampling technique involves the use of samples of relatively small size.

The measurements above are made automatically by a computer-controlled testing system which, in and of itself, is known. One such system, described in the context of testing a somewhat sophisticated article, namely a color kinescope, is described in copending application, Ser. No. 653,083, Digital Computer Controlled Test Sys- 3 tem, filed July 13, 1967 by Walter Endres Bahls,l et al. and assigned to the assignee of the present application.

Hopefully, the elements tested are within specifications and, if so, they are selected for the manufacture of finished products. As a second alternative, the lot of elements may not fall within specifications but may possibly still be usable for the manufacture of finished products whe'n combined with the other lots of elements. 1f so, this lot is provisionally accepted for use. As a third alternative, the elements may be so far out of specification, that they are not usable. In this case, the sampling technique employed will indicate that the entire lot of elements should be rejected, either to be returned to the supplier or to be tested in their entirety so that only those elements in the lot which fall within specifications may be retained and the others discarded.

In the system of the present invention, a lot of elements may be rejected for any one of a number of reasons. For example, if a sample of elements being tested indicates there is an excessive population in the lot which have values of a measured parameter greater than the value of that parameter at 4s, where s is the standard deviation for that parameter, that lot is rejected. The expression, standard deviation (sometimes also indicated by the Greek letter sigma), refers to the amount of scatter or dispersion or, thought of another way,A the degree of concentration of the measurements made of a given parameter. A lot may be rejected also if the mean value or central tendency t of a measured parameter differs from the ,u called for in the specifications by greater than a given amount. The terms p. and s and others mentioned later are defined more precisely by means of simple equations in any standard text on statistics as, for example, S. S. Wilkes, Elementary Statistical Analysis, Princeton University Press, 1951.

A lot of elements may be conditionally acceptable if, for example, it has an excessive population with values of a measured parameter between the measured values of that parameter at the 3s and 4s points and/ or if its measured central tendency ,um is as indicated in the following expression:

where ,us is the specified tendency and ss is the specified standard deviation. The term measured above is placed in quotes because what is actually measured is a voltage, current or the like, indicative of a parameter and it is from a group of such measurements that a quantity such as pim or sm is calculated.

As already mentioned, samples of the elements in all lots A M are tested. Those lots of elements which the tests indicate are fully acceptable and those lots of elements which the tests indicate are provisionally acceptable are then placed together in a storage area. In one practical situation to be discussed shortly, a sufficient number of elements in each lot is stored to permit the manufacture of 500 finished products. This may represent the number of products to be made in one eight-hour factory shift.

The te'sts made of the lots of elements A M .indicate not only whether these lots meet specifications or provisionally meet specifications, but also the actual parameter distribution characteristics of the elements of each lot. For example, a lot of resistors which have a nominal resistance of 100 ohms may be found to have a normal, that is, a Gaussian distribution with a central tendency of 98 ohms and with 65% of the resistors having a value between 97 and 99 ohms. This information is calculated by the same digital computer which controls the operation of the test stations which measure the resistance or other parameters of interest. From this information, the computer also calculates the performance which will be exhibited both by the subassemblies made from the elements and by the finished products made from these subassemblies.

Of course, the performance of the finished products should meet a marketing standard initially stipulated fory the product. For example, in the case of a radio receiver, it should have a certain gain, a certain selectivity, a certain freedom from noise and so on. However, the tests of the lots of components may indicate that the finished products will have parameter values which differ from the marketing standards in a sense such that the finished products will be better than those originally called for. These values are made use of in testing the finished products to determine not only whether they are marketable but also whether the manufacturing process is operating in the manner it should. In other words, if a finished The computer indicates, with great precision, what pert centage of the finished products is expected to meet the marketing standards. For example, in a factory run of 500 receivers, the computer may indicate that 492 of the receivers will be marketable and eight of the receivers not marketable and therefore not acceptable. Calculations have been made to indicate what percentage of final? products have to be good to make the manufacturing process a profitable one. If this percentage is met, then the lots of elements selected are used to manufacture the subassemblies and final products.

The calculations performed by the computer may indicate that less than the desired number of final products will be acceptable, if the lots of elements initially placed together are employed in the manufacture of the finished product. The digital computer is programmed to calculate not only this information but also the actual performance characteristics to be expected of those finished products which will be unacceptable. The computer is also programmed to `compare the operating parameters calculated for the finished products with those desired for the finished products and to indicate the components responsible for the unacceptable performance.

It should be recalled at this point that some of the elements accepted initially were accepted only provisionally and it generally will turn out that the unacceptable performance of the finished product is due to this group of elements. When the printer or other visual indicating device associated with the computer indicates the elements which are inadequate, they are replaced with a second group of elements of the same type. This second group of elements is tested in exactly the same way as the first group `was tested and if they are acceptt able or provisionally acceptable, they are placed together with the remaining group of elements. Thereafter, the same procedure as above is repeated.

It should be mentioned here, that at this point, not only is it known which elements are poor but also what characteristics of these elements must be improved. It may be found, in practice, that it is sometimes more economical to place more rigid specifications on a relatively nonexpensive element and relax the requirements for a more expensive element and still produce a product which is better than and less expensive than the product made according to the original design. For example, in the manufacture of a radio receiver, it may be that a conditionally accepted lot of ganged capacitors which cost $1.50 per unit is causing too many rejects to occur. This lot, in some cases, may be retained and a good lot of resistors costing one cent per unit replaced by a better lot yof resistors, perhaps at a slight increase in price per resistor, to reduce the number of rejects to an acceptable level, and considerable money saved in the process.

In accordance with the manufacturing technique of the present invention, at the time the performance of the subassemblies and the iinal assemblies is calculated, appropriate limits for the programs of tests for the subassemblies and nal assemblies are automatically calculated. These programs of tests are subsequentially employed in the test stations for checking the performance of the subassemblies, and final assemblies, as is discussed shortly.

Major portions of the system of the present invention are shown in FIG. 2. The dashed lines indicate the paths along which materials flow. The solid lines indicate electrical interconnections and each single line represents a multiple conductor cable.

The many components used in the manufacture of a mass produced product arrive at the region indicated at the upper left of the FIG. 2. The iirst step in the manufacturing process is to test the components and this involves determining the statistical distribution with re- `spect to certain performance criteria of various parameters of the incoming parts and keeping a record of this information. The testing is performed at components test stations 10.

An operator may select a random sample of incoming components and place this sample in a special testing board. To give a simple example first, in the case of resistors, perhaps 40 or 50 resistors may be chosen from a lot of 500 to several thousand resistors and these selected resistors placed between a corresponding number of sets of terminals on the board. The board also may include a means for identifying the circuit elements to be tested, as for example, a set of contacts which will indicate to the test station that: the items it is to test are resistors which have a certain nominal or mean value (,Lt) such as 100 ohms, a certain standard deviation s such as 2 ohms, with a known distribution such as Gaussian.

After boards such as the above are assembled, they are plugged into one of the test stations within block 10. The test station is operated under the control of the local control equipment 12 which is located in the factory environment and the local control equipment, in turn, is controlled by a digital computer 14 of the stored program type. The digital computer, which may be an RCA Spectra 70-45 or other commercially available machine, is normally located in an air-conditioned room and it may be several hundred feet away from the factory door and the local control equipment.

The operation of a test system 'of this type is quite analogous to that of the computer controlled color test system described in the Copending application. In brief, in response to the component identification data supplied to the digital computer 14 through the local control equipment 12, the computer selects from its memory a program of tests suitable for these particular cornponents. The program may already be in the main memory of the computer 14 or it may be stored in a piece of peripheral equipment such as a disc iile which is located within block 16. If the program is stored in a disc le, it is rapidly transferred to the main memory of the computer and the computer then causes the local control equipment to make the test station perform the tests which are required. For example, the local control equipment may cause the test station to apply a predetermined current, in succession, to the resistors being tested and each time a current is applied to a resistor, a measuring circuit at the test station may measure the voltage appearing across that resistor. The successive voltages thereby obtained are applied to an analog-to-digital converter in the local control equipment 12 and translated there to successive binary words.

When employing the sequential sampling technique, after each measurement of an element, such as a resistor, is made, the computer performs calculations on the binary Word (s) indicative of that measurement and of measurements of previous elements of the same sarnple. One of these calculations involves a statistical determination of when a sufficient number of elements in that sample have been tested to provide a reliable estimation of the characteristics of interest of the entire lot of elements from which the sample was chosen. If the sample size is tentatively chosen to be 5() elements, as an example, it may very well be that the computer will decide that a reliable estimate has been made after only 15 of these elements or less have been tested. In this case, it so signals the operator and does not test the remaining elements of the sample. On the other hand, it occasionally occurs that the 50 elements of the sample may not provide the desired data with suicient certainty. In this case, a signal is applied back to the test station to indicate to the operator that another sample (another group of elements) must be chosen from the same lot and tested. The tests and calculations occur very rapidly-within a fraction of a second.

When the computer 14 is satisfied that the tests made have provided sufcient data for an accurate determination of the characteristics (standard deviation, type of distribution curve, its central tendency, its skew, and so on) of all elements in the lot from which the sample was chosen, it so indicates at a printer or the like located at the test station within block 10 which is testing that sample, so that the operator may proceed to the next lot of parts. It also indicates whether the entire lot is acceptable, or whether it must be rejected. The calculations necessary to obtain the values of the various statistical quantities are in themselves straightforward (again see any text on statistics), and readily are programmed on any general purpose machine as, for example, the RCA Spectra 70-45. The decision rules for determining whether a lot is acceptable or not involves comparisons of calculated data with data relating to a, s and so on stored in the computer memory and also readily are programmable.

There may be up to several hundred or more components employed inthe manufacture of a relatively complex article. Each lot of components is tested by sequential sampling techniques in the manner described above and, when the testing is completed, the accepted or provisionally accepted lots of components are grouped together and tentatively placed in a storage area. The storage area is shown at 18 in FIG. 2. It may contain a sufficient number of sets of lots of components for from one to, say, twenty factory runs, that is, from one to twenty or so eight-hour shifts of production. The number of sets of components will depend upon economic factors such as the cost of inventory, the cost of storing the parts, the possibility of running short and losing production time and so on. In the manufacture of a complex article such as a radio receiver, only a small number of sets of lots, such as three, need be present at any particular time, provided there is a suflicient back-up of untested components. For other articles, a larger number of sets of lots may be preferable. For purposes of illustration, twenty sets are shown in FIG. 2.

The last set of lots of components tested is legended set 20 in FIG. 2 and it consists of the m groups of components needed to manufactureSOO products such as receivers. This set 20 is a group of interrelated components which will move together through the production system. Similarly, the set 19 which was previously tested and stored is a group of interrelated elements, and so on.

The selection of components just described is a tentative selection. At the time the various components are placed together, the digital computer 14 has stored in its memory data relating to the values of various parameters of the components and their distribution. This computer also has stored in its memory, a program of calculations to be performed on this data which will determine a number of different things. First, it will determine what percentage of the completed receivers will fall within specifications and what percentage will not. Hopefully,

7 a suicient number of the components will fall within specifications that it will be economical to go ahead with the manufacture of the receivers from that set of lots 20 just selected. However, if the results obtained by the computer indicate that too small a percentage of the finished receivers will be acceptable, this will mean excessive costs for reworking the unacceptable products and a corresponding excessively high cost of manufacturing.

The stored program in the computer will automatically indicate whether or not the set of lots 20, for example, is a satisfactory set. If the set is satisfactory, it is bonded, that is, it is certified to be suitable for manufacture and no components are thereafter either added to or removed from the set until manufacturing starts. If the set of lots is unsatisfactory, the computer determines from the test data it has accumulated, why there will Ibe an unusually high percentage of unacceptable nished products.

It should be mentioned that the determination of Whether or not an acceptable distribution of iinal products will result from a particular set of lots is made immediately after a complete set of lots has been measured. No measurements of another set of lots are made before this determination is completed. For example, measurements of the set of lots 20 will not begin until set of lots 19 has been bonded At the time the analysis is made in the present system, as contrasted to what is done in the system of the copending application, the nal products have not been made but instead the values of parameters which the final products would have, if the manufacturing were allowed to proceed, are calculated. To give a simple example, prior to the time manufacturing starts, the computer 14 may indicate that a lot of resistors which was accepted for set 20 but which perhaps did not quite meet the specifications originally set forth for those resistors should be replaced with resistors of higher mean value. As a second example, the computer may indicate that the intermediate frequency transformers have insufficiently broad band-passes, and so on. In any such case, before manufacturing starts, the lot of components within a set indicated to be inadequate is removed and replaced with another lot of components which, hopefully, is compatible with the remaining components. This substituted lot of components is tested at 10 in the same manner as already described and the computer 14 then makes another set of calculations to determine whether a sufficiently high percentage of the final products is acceptable.

After determining that a set of lots may be bonded, the computer 14 also determines what the performance of the audio boards (each such board includes a number of stages of audio amplification), the radio frequency boards (each such board includes, for example, several radio-frequency stages and the local oscillator), and other subassemblies should be and also what the performance of the complete receiver should be and it also determines the limits to be employed in the programs of tests which measure these performance parameters. These calculations, like the ones just described, are based on the statistical distribution data stored in the computer. After the test limits for a particular set of lots such as set are determined, this information is stored in one of the peripheral equipments as, for example, on a magnetic disc or a drum, or a magnetic tape. When, at some later time, a particular set of lots of components is manufactured into subassemblies and the subassemblies made into the finished receivers, this program is calledup by the computer 14 and employed to direct the operation of the various test stations.

For most of the tests, changing the test limits involves employing the same values of stimuli but sensing for different values of signals indicative of the parameters being measured. For example, in testing one lot of resistors, a current of one milliampere may be employed and the measuring amplifiers set to sense a voltage of one volti.05 volt. For another lot of resistors, the same value of stimulus (current, in this case) may be employed but the measuring equipment set to sense a voltage of 0.95 volti.05 volt.

There are some tests, however, analogous to some of the tests described in the copending application in which a predetermined value of sensed signal must be obtained. Here, in order to obtain this value of sensed signal, the stimulus is changed in accordance with a predetermined program until the desired value of sense signal is produced.

At the beginning of a factory shift, a bonded set of components is removed from the storage area 18 and is then manufactured into the finished receivers. The manufacture is illustrated to occur in several different steps. First, subassemblies are lmanufactured and this occurs in the area indicated by block 20. Each subassembly is tested at the subassembly test stations 22. Preferably, only the transfer characteristic of the subassembly need be measured. In other words, each subassembly is treated as a black box and the test station applies a certain set of inputs to this box and measures the corresponding outputs produced by the box. The values of the inputs are determined by the program and, as already mentioned, they may, in some cases, be different for the subassemblies made from the different sets of lots. Correspondingly, the

distribution of outputs expected in response to the stimuli applied to the various subassemblies will, in many cases, be different for the different sets of lots.

The signals sensed by the test stations 22 which are indicative of the parameters being tested, are converted to binary information and compared with stored binary information in the manner already discussed in connection with test station l0. A determination is then made by the computer as to whether the subassembly being tested is acceptable or not. If a subassembly is not acceptable, means may be provided at the test station for so indicating to the operator. The printer associated with the computer or, as an alternative, a printer located right at the test station (Within block 22) may be employed automatically to print out what has caused the subassembly to fail its tests. This print-out may be employed to assist in repairing the subassembly, if repair is possible.

After the testing of the subassemblies is completed,

those which are acceptable are assembled into complete receivers at 24. The complete receivers are subsequentially tested at test stations 26 which, like the other test stations,

are also under the control of the digital computer 14., Again, as in the case of the subassembly test stations 22,`

the receiver test stations will either accept or reject the finished receiver and, if rejected, will indicate the component or subassembly of the receiver which is not operating properly.

In the computer-aided manufacturing system of FIG. 2, there may be separate power supplies for each test station or there may be a common power supply which is time-shared among the test stations. Both types of power supplies are described in the copending application. For purposes of illustration, a time-,sharedpower supply is shown at 28 in FIG. 2. This block also includes the routing circuits as discussed in the copending application.

In the foregoing description of the operation of the system of the invention, for the sake of simplicity, the testing of a lumped circuit element such as a resistor is discussed. These days, this illustration may be somewhat too simple. Instead of elementary circuit elements such as resistors, capacitors and the like, modules consisting of many different elements, some active, some passive, are often used to make an article such as a radio receiver or other circuit. One such module is illustrated in FIG. 3. It is a one-stage stereo amplifier consisting of the circuit elements shown, laid down on a ceramic substrate and having the appearance of a small block or package with eight leads. This package is tested for various parameters in the same general Way as described for the resistor, however, the tests are considerably more sophisticated. Some of these are discussed below by way of example.

FIG. 4 illustrates the test made at the component test station, under program control, for low frequency gain of the module of FIG. 3. At this test station, a 70 Hertz, 0.1 volt, alternating voltage source e1, 2 is connected at one terminal to leads 1 and 2 and at its other terminal to ground. Lead 3 is connected directly to ground. A +25 volt direct voltage source, shown as a battery, is connected to lead 5 and others of the leads are connected through resistors to ground, as shown.

The component test station measures the output voltages at leads 4, 6, 7 and 8, that is, the output voltages e4, es, e, and e8, respectively. As soon as these measurements are completed for a component, the computer performs a number of calculations. First, it determines the ratios e4/e1, 2, eti/e1, 2, eq/el, 2 and eg/el, 2. These numbers may be termed random variables and are indicative of four different gain parameters of interest. For example, e4/ e1, 2 is a measure of low-frequency voltage gain of the transistor Q2; e6/ e1, 2 is a measure of the same parameter but it also is a measure of the relative values of resistors R7 and R8, and so on.

From the calculations above, the computer then calculates the mean value u of the four random variables. It does this by adding the successive random variables and dividing by the number of measurements which are made. For example, if measurements are made of 25 modules of FIG. 3 and therefore 25 measurements of e4, and 25 calculations have been made of the random variable :e4/e1, 2, these 25 values of e.2/e1I 2 are added and divided by 25 by the computer, under program control, to obtain the mean value p. of this variable.

After the mean value s have been determined for the various random variables, the computer, under program control, calculates the standard deviations for these variables. The equation for the standard deviation is:

where x1 is the value of this random variable for the first sample, x2 for the second sample xn for the nth sample and n equals the number of samples.

TABLE I Random variable u s 4. 22 0. 117 0. 759 0. 0212 0. 759 0. 0212 e s/o 1,2 4.22 0.117

The comparisons made by the computer will indicate Whether the lot of circuit modules being sampled has a low-frequency gain which is acceptable or which is provisionally acceptable or which is not acceptable. Some of the rules for this decision are given above and are illustrated below in the discussion of FIG. 6.

The computer does not directly calculate the shapes of the distribution curves for the random variables discussed above. (In the particular example being discussed, the desired shape is a normal distribution.) However, the calculations made to determine the deviation s, in an indirect way, indicate whether the distribution of parameter values is or is not that called for by the specifications.

The high frequency gain of the module of FIG. 3 is tested in a manner similar to that shown in FIG. 4. All of the connections are the same, however, the voltage e1, 2 is 0.1 volt at 10,000 Hertz rather than at 70 Hertz. Similarly, the specified values of ,a and s are slightly different than those given in the table above.

FIG. 5 illustrates the tests made of the module of FIG. 3 to determine the gain, the separation, and the input impedance of the upper channel (the one with transistor Q1) of the FIG. 3 circuit. Here, the stimulus e1 is applied only to lead 1 and has a value of 0.1 volt at 1,000 Hertz. The component test station measures the voltages e4, e8 and en, and then calculates the random variables elo/e1, e/em and {z8/e4. For this particular circuit, the specified values for ,a and s for these random variables are:

It may be observed from Table II above that in one case a minimum value of ,u is specified. This value is simply an indication of the amount of separation which must be present between the two channels when one of the channels has an input and the other does not.

In addition to the various tests given above, the module of FIG. 3 is also tested for other parameters. For example, tests are made of direct-current leakage, gain, separation, and input impedance of the lower channel, clipping level, and noise level. As the tests discussed in detail above are sufficiently representative, these other tests are not illustrated separately.

After the random variables above have been measured and the various calculations carried out to determine the values of a, s and so on for these random variables, the computer then determines whether the set of the lots into which the components have tentatively been placed may be bonded. This determination will be illustrated only for a single random variable, namely the gain of one channel of a stereo amplifier. However, it is to be understood that similar determinations are made for all random variables of interest.

The amplifier is illustrated in FIG. 6 and it is shown to consist of five components, P1 through P5. Three of the components are, themselves, amplifiers and two are tone control circuits. Each part P may, for example, be a circuit on a ceramic substrate, just like the circuit of FIG. 3. In this case, the FIG. 6 circuit may be considered to be a subassembly and this subassembly may be part of a larger system such as a radio receiver'or the circuit may be considered to lbe a final product made from elementary components. As a third alternative, one or more of the blocks in FIG. 6 may, itself, be considered a subassembly which previously was fabricated by soldering together transistors and other circuit elements and the entire circuit of FIG. 6, a finished product in a separate chassis Which is sold as a stereo amplifier. In any of these cases, the principles of manufacturing are the same.

The gain G of the channel of interest of the amplifier of FIG. 6 is given by the following equation:

G=A1A2A3A4A5 (3) where A1=the voltage gain of stage P1, A2=the voltage gain of stage P2,

and so on. In Equation 3 above, A1, A2 A5 may be In addition, the measured deviation sm for each component should be less than the specified deviation ss, as shown in the following equation:

Table III below is a set of specifications for the amplilier illustrated in FIG. 6.

The so-called management limits mentioned previously are determined in the following way. Let ng equal the mean value of the gain of the ve stages of the amplifier. This quantity ,ug can be calculated from the following equation which is derived from Equation 3:

lLgMMZ/Lslft Where n1=the mean value of the gain of stage P1, ,u2-:the mean value of the gain of stage P2,

lFrom Equation 3 and the specified mean values of gain ,as given in Table III, the actual values of B can be determined in the following way: B1=aG/aA1=A2A3A4./15=(0.2) (6) (0.3) (s)=2.88 (s) B2=G/5A2=A1A3A4A5=(5) (6) (0.3) (8)-72 (9) B3=2.4 (10) B4=48 (11) B5=1.8 (12) From Equations 7-12 and the values of ss given in Table III, the value of .sg can be determined and it is found to be:

From Equation 6 and the values of n given in Table III, the value of ,as is found to be:

It has been determined that the upper and lower acceptable limits LL and LU, respectively, for the gain should be:

These upper and lower limits are the so-called management limits. The factors taken into consideration in arriving at these limits are concerned with the Variations expected in ,um and other factors which need not be discussed here.

After a set of lots is measured, upper and lower limits for the different parameters of interest for that set of lots are calculated by the computer in the same way as discussed above, however, the measured values of ,a and s are used instead of the specified values. To bond a set of lots, the computer must find that the calculated upper limit for each random variable of interest is equal to or less than the management upper limit and the calculated lower limit for each such random variable is greater than or equal to the management lower limit.

The following numerical illustrations will serve to illustrate this. Suppose still that gain is the parameter of interest. Suppose also that the various voltages of interest have been measured and the following values of ,u and s calculated.

TABLE IV Stage n s P1 ;L1=5.12 81=0.13. P2 #2:0203 S2=0.007. P3 u3=5.8 83=0.1. P4 p4=03 S4=0.01. P5 p5=81 85:02.

From Equation 6, the mean value of the gain ,ig is found to be ag=l4-580 and from Equations 7-12, the standard deviation sg for the gain is found to be equal to sg=0.9075. Therefore, the calculated upper limit for the gain is LU: l4.58+3(0.9075)=17.30i2 and the calculated lower limit is LL:14.583(.9075)=11.858. In this instance, the calculated upper limit 17.302 is lower than management upper limit 17.673 and the calculated lower limit 11.858 is greater than the management lower limit 11.127. Therefore, with respect to the gain parameter, the set of lots may be bonded. Moreover, when testing the manufactured amplifier of FIG. 6` for this parameter, the test limits with which the measured limits will be compared, will include the calculated limits just specified as well as the management limits. If the finished product meets (is within) the management limits LU=17.673 and LL=11.127, it may be (but is not necessarily) accepted even if it is not within the narrower limits of 17.3 and 11.8 just calculated. It will be accepted if close to the narrower limits. It will not be accepted if the actual measurements of the manufactured amplifier indicate limits well outside of the calculated limits but within the management limits. In either case, the failure to fall within the narrower limits indicates that the manufacturing process is not operating in the way it should and that corrective action should be taken. And in the latter case, it may indicate a relatively serious failure in the manufacturing process which would not show up until the amplifier Iwas shipped and this would mean later failures in the eld, later repair costs, dissatisfied customers and so on.

As a second example, suppose in a set of lots of components, one part P3 is out of specifications but all other parts are well within specifications. This example is illustrated in Table V below.

TABLE V Stage u s 1 :Out 4of specifications.

When the same type calculations as discussed above are performed by the computer, it will come up with the following results:

These results meet all of the management requirements for the gain parameter and this set of components is ac ceptable for bonding in this respect.

In a third example, suppose one of the parts P3.is out of specifications just as in the last example above.

13 14 However, the other parts are barely within specifications. 3. A method of manufacturing products comprising the Now the situation is as shown in Table VI fbelow. steps of:

TABLE VI specifying the mean value as, the standard deviation ss, and the shape of the distribution curve of parameters of interest of lots of elements to be used in the gig-ge manufacture of the products; s,=f31 sampling the lots of elements to be employed in manu- ;ggh facturing the products, some of which lots may ibe within specifications and some of which may be outlzoiit'of specifications lo side of specifications, and determining from these The computer now provides the following results: samples the actual values um, sm of the parameters 'u 14 4 of interest of each lot;

gfor each parameter of interest of each lot of elements, sg=l.l2 if nm (us-ss) or if ,um (us-tss), rejecting that lot LU=17 76` 15 of elements, and if sm ss, rejecting that lot of elements, and if more than a given number of the ele- LL=1104 ments of a lot have a measured value of a parameter Now the measured lower limit is less than the managegreater than the Value of that Parameter at 4Ss, rement limit of LL=11.127 and, in addition, the measured lecting that lot 0f elements; upper is greater than the management of Substituting fOr each rejected lot Of elements any, a LU -17673 Either of these discrepancies is enough to new lot which has parameters of interest such that disqualify the set of lots. This set of lots cannot be (l/sSs) lLm (/Lsl-Ss), Sm ss, and less than agiVen bonded, number of the elements of each lot have a measured As a final example, suppose the components were the Value 0f a Parameter less than the Value Of that same as those illustrated in Table IV except for the part Parameter at 45's; P3. Assume here that its mean value n3 is out of speciticadetermining from the measured values of parameters of tion and is equal to 4. For this set of lots, the computer the acceptable lots of elements, some of Which may will calculate the following Values: be outside of specifications, the values and their dis- 1009 trlbution of performance parameters the products 'ue- 30 manufactured from the acceptable lots of elements se=.908 t will have; and LU=12-81 comparing these performance parameters with previously established performance limits and, (a) if the LL=737 former are within the latter, regardless of whether Now, the upper limit is within specifications but the lower one or more of the lots is outside of sPeciiications, limit is not. This set of lots therefore cannot be bonded. manufacturing the Products from said lots 0f ele- It should be clear from this example that what must ments, (h2 if the Performance Parameters are out' be done is to substitute for the part P3 a part P3 which Side of said Previous established limits, Substituting is within specifications, insofar as its central tendency 3 is 40 for. at least one of the lOtS Of COmPOIleIltS, a lot concerned which will make the performance parameters of the What is Claimed is; products fall within said previously established limits, 1. A method of manufacturing products comprising the and then manufacturing the Products from the lots Steps oft of components.

specifying the values and their distribution of param- 4- A method of manufacturing Products comprising the eters of interest of lots of elements to be used in the steps o f manufacture of the products; specifying the values and their distribution of param- Sampling the lots of elements to he employed iu manu. eters of interest of lots of elements to be used in the facturihg the products, Some of which lots may he manufacture of the products, which values and their within specifications and some of which may be outdistribution Will enable the Products to :he Within a side of specifications, and determining from these Predetermmed marketing standard; samples the actual values and their statistical dis- Sampling the lots of elements to he employed in manutribution of parameters of interest of each lot; factoring the Products, some of Which lots may he determining from these measured values, the values Within specifications and some of Which may he out' and their distribution, of performance parameters Sido of sPecincations, and determining fl'Om these that the products manufactured from the sampled samples the actual values and their statistical dislots of elements will exhibit; aud tribution of parameters of interest of each lot; comparing these performance parameters with nrevi determining from 'these measured values and their staously established performance limits and, (a) if the tistlcal d1str1but1on, the test limits to be employed in former are within the latter, regardless of whether testing the Performance of the Products manufacor not a lot is outside of specifications, manufacturttlftjd from the sampled lots of elemelltS, Said teSt mg the products from said lots of elements, (b) if llmits normally not being 1dent1cal with said marketthe performance parameters are outside of said pre ing standard but not falling outside of said marketvious established limits, substituting for at least one mg Standard; of the lots of componentsa not necessarily a tot one manufacturmg the products from said lots of elements; side of said limits, a lot which will make the perand formance parameters of the products fall within said testing the Performance of the manufactured PrOdUCtS previously established limits, and then manufactur- ,Sitlg Said test limits, a departure from Said test ing the products from the lots of components l1m1ts being'indicative of possible deterioration in the 2. The method of claim 1 and further including the manufacturmg Process t step of; 5. A method of manufacturmg products in which eletesting the performance of the manufactured products ments are first fabricated into subassemblies and the subusing test limits based upon the performance paramassemblies are then interconnected to form the final prodeters determined from the measured values and their ucts comprising the steps ofi distribution of the parameters of interest of said lots Specifying the values and their distribution of paramof elements. eters of interest of lots of elements to be used in the l manufacture of the products, which values and their distribution will enable the products to be within a predetermined marketing standard; sampling the lots of elements to be employed in manufacturing the products, some of which lots are within specifications and some of which are outside of specifications, and determining from these samples the actual values and their statistical distribution of parameters of interest of each lot; manufacturing subassemblies from the lots of elements and the final products from the subassemblies; and

testing the performance of the subassemblies and final products using test limits calculated from the actual values and their distribution of the parameters of interest of said lots of elements, said test limits normally not being identical with said marking standard but not falling outside of said marketing standard, a departure from said test limits being indicative of possible deterioration in the manufacturing process.

6. .A method of manufacturing products in which elements are first fabricated into subassemblies and the subassemblies are then interconnected to form the final products comprising the steps of:

specifying the values and their distribution of parameters of interest of lots of elements to be used in the manufacture of the products;

sampling the lots of elements to be employed in manufacturing the products, some of which lots are within specifications and some of which are outside of specifications, and determining from these samples the actual values and their statistical distribution of parameters of interest of each lot;

calculating from the actual values and their statistical distribution of parameters of interest of each lot, the number of final products manufactured from said lots which will be acceptable and, if said number is lower than a given value, replacing the one or more of the lots of elements responsible for the relatively low number of acceptable final products;

manufacturing subassemblies and final products from the lots of elements; and

testing the performance of these subassemblies and final products using test limits calculated from the actual values and their distribution of the parameters of interest of said lots of elements.

References Cited Lapp Insulators for 1928, Catalog `#4, March 1928.

RUDOLPH V. ROLINEC, Primary Examiner E. L. STOLARUN, Assistant Examiner U.S. Cl. X.R. 324--73 

